For your bugs (from LFEAGIN at CALSTATE.BITNET), I get
(run in Sun verison 1.2):
In[1]:= Limit[ x/Sqrt[x^2], x->-Infinity ]
Out[1]= 1
In[2]:= Integrate[x b^(a x), x ]
a x Log[b] 1 x
Out[2]= E (-(----------) + --------)
2 2 a Log[b]
a Log[b]
In[3]:= D[%,x]
a x Log[b]
E a x Log[b] 1 x
Out[3]= ----------- + E a (-(----------) + --------) Log[b]
a Log[b] 2 2 a Log[b]
a Log[b]
In[4]:= Expand[%]
a x Log[b]
Out[4]= E
When you ask Mathematica to Plot the function x/Sqrt[x] say from
-1 to 1, you get the step function with jump at 0, but the Limit
function does not give -1 as it probably should.
In the second example, it is clear that the rules for E and Log's
are not automatic, but could easily be programmed in.
I note that Maple also gives 1 for In[1], But does simplify Out[4]
back to the x b^(a x).
Macsyma gives -1 for the limit, but does not simplify
the exponential automatically.
Steve
-------------------------------------------------------------------------
Steven M. Christensen
Senior Research Scientist (Theoretical Physics)
National Center for Supercomputing Applications
Beckman Institute for Advanced Science and Technology
University of Illinois at Urbana-Champaign
Urbana, Illinios 61801 USA
Phone: (217) 244-0544 (with answering machine)
Phone: (217) 244-0072 (main NCSA number for messages to a human being)
FAX: (217) 244-2909
Email: stevec at ncsa.uiuc.edu (Internet)
Email: 14008 at ncsavmsa.bitnet (Bitnet)
-------------------------------------------------------------------------